Question

explain how to add complex numbers. give an example.

choose the correct answer below.

a. to add complex numbers, subtract the real parts and add the imaginary parts. for example, (4 + 5i) + (2 + 3i) = 2 + 8i.

b. to add complex numbers, add the real parts and subtract the imaginary parts. for example, (4 + 5i) + (2 + 3i) = 6 + 2i.

c. add complex numbers just like adding polynomials by using the distributive property. for example, (4 + 5i) + (2 + 3i) = 4(2 + 3i) + 5i(2 + 3i).

d. add complex numbers just like adding polynomials by combining like terms. for example, (4 + 5i) + (2 + 3i) = 6 + 8i.

Explanation:

To add complex numbers, we combine like terms (real parts with real parts and imaginary parts with imaginary parts), similar to adding polynomials. Let's analyze each option:

• Option A: Says to subtract real parts, which is incorrect. The real parts should be added.
• Option B: Says to subtract imaginary parts, which is incorrect. Imaginary parts should be added.
• Option C: The example shown is for multiplying complex numbers (using distributive property for multiplication), not addition. So this is incorrect.
• Option D: Correctly states that we add complex numbers by combining like terms (add real parts and add imaginary parts). For the example \((4 + 5i)+(2 + 3i)\), we add the real parts \(4 + 2 = 6\) and the imaginary parts \(5i+3i = 8i\), resulting in \(6 + 8i\).

Answer:

D. Add complex numbers just like adding polynomials by combining like terms. For example, \((4 + 5i)+(2 + 3i)=6 + 8i\).